FCAT Packet #5
FL.MA.6.A.3.2
Write, solve, and graph one- and two-step linear equations and inequalities.
Vocabulary:
Equation- mathematical sentence showing two expressions are equal.
Solution- value for a variable.
Solving Equations
-ALL WORK MUST BE
SHOWN ON A SEPARATE
SHEET OF PAPER!
-NUMBER ALL PROBLEMS
AND CIRCLE ALL ANSWERS!
-PUT ALL ANSWERS IN THE
ANSWER COLUMN.
To solve two-step equations, you can balance the equation by getting the variable by itself. First, undo any addition or subtraction.
Then undo the multiplication or division.
5y -2 = 18
+2 = +2 Add 2 to both sides to keep the equation balanced
5y = 20
5
5 Divide both sides by 8 to get the variable alone on one side.
y
=4
Check your work: If y=4, then 5∙4 – 2 = 18
18 = 18 √
Writing One-and Two-step Equations
An example:
Maggie is y years old. Kate is 15 years old. The total of Maggie and Kate’s ages equals 24. Write an equation that you would use to
find Maggie’s age.
By looking at this problem, you should know that if you add Maggie’s and Kate’s ages you would get 24. Therefore, the
equation you would write would be:
y + 15 = 24
Another example:
Charlie earns $6 for every hour that he works. He earned a total of $30. Write an equation that you would use to find how many hours
(h) he worked.
By looking at this problem, you should know that you would multiply the amount he earns per hour ($6) by the number of
hours he actually worked (h) to get his total pay ($30). Therefore, the equation you would write would be: 6h = 30
Sometimes you have to do more than one operation in a problem.
Bobby hit the baseball 3 more than twice than number of times Paul hit it. Let p represent the number of times Paul hit the baseball.
What equation would you write to represent the number of times Bobby hit the baseball.
By looking at this problem, you know that first you must multiply the number of time Paul hit the baseball (p) by 2. Then you
must add 3 to this number. Your equation would be: 2p + 3
Try these on your own:
1) 5x – 4 = 16
2) 8 + 7m = 50
3) 8q – 6 = 50
4) 9k – 4 = 32
5) Mrs. Stevens earns $18 an hour at her job. She had $171 after paying $9.00 for subway fare. Write and solve an equation to find
how many hours Mrs. Stevens worked.
6) There were 10 birds in the tree in my backyard. The number of cats under the tree was 6 less than twice the number of birds. Which
equation shows the number of cats (c) under the tree?
2 x 10 = c
2 x 10 – 6 = c
2(10 – 6)=c
2 x 10 + 6 = c
7) Harry needs to earn $150 to get a new bike. He earns $5 per hour for babysitting his little sister. Using the equation 5h = 150, how
many hours does he need to babysit in order to buy his new bike?
8) Mary is selling cookies. She earns $3 per hour and $0.10 for each box sold. The equation m = 3h + 0.10b can be used to find the
amount of money Mary earns. If m = money, h = hours selling, and b = boxes sold, how much money would Mary earn if she sells for
20 hours and sells 150 boxes of cookies?
9) Pedro is saving money to buy a new skateboard that costs $149. He plans on saving $15 each week. Write and solve and equation
to find in how many weeks Pedro will have enough money to buy a new skateboard.
Inequalities
Sometimes the information shows that things are not equal and you must use an inequality sign (<, >, ,  ) rather than an equal sign.
Remember these tips: < looks like an L so it is the less than sign. > means greater than since the large opening is shown first.
 means less than or equal to.
 means greater than or equal to.
For example: Mary is 4 feet tall. Her brother Karl is shorter than Mary. Write an inequality to show how tall her brother could be.
Karl < Mary
so Karl < 4
so K < 4
Another example: Susan had the most money in her piggy bank at home. She had $52. David had the least amount of money in his
piggy bank at home. He had $4. Write an inequality to show how much money all the others in the class could have.
Susan > others > David or S > o > D or 52 > o > 4
Another example: John knew he would earn at least $10 for mowing the lawn. If he did more than just mow, he would earn more than
that. Write an inequality to show how much money (m) John could earn. m  10
Finding Solutions of Inequalities
To determine if a number is a solution to an inequality, simply plug in the number for the variable and solve. If the sentence is true,
then the number is a solution.
1 + f < 7 ; 5, 6, 7
1+ 5 < 7
6 < 7 True, so 5 is a
solution.
1+6<7
7 < 7 Not true, so 6 is NOT
a solution.
1+7<7
8 < 7 Not true, so 7 is
NOT a solution
Practice: Determine which number or numbers could be a solution of the inequality.
10) 5 – h ≥ 2 ; 2, 3, 4
11) g – 3 > 4 ; 6, 7, 8
12) Yes or No q -2 > 16, q = 20.
13) Yes or No
25 ≥ 5u , u = 5.
Writing Inequalities
You must be over 12 years old to ride the go-karts.
YOUR AGE
IS OVER 12
Words
Practice:
14) You must be older than 13 to play in the basketball league.
15) You must be at least 18 years old to vote.
Variable
Let a = Your Age
16) To use one stamp, your letter must be under 3.5 ounces.
17) The movie will be no more than 90 minutes in length.
Inequality
a
>
12
Graphing Inequalities
O = an open dot means the number is NOT included in the graph
n>9
n ≤ 10
5
5
6
6
7
7
8
8
9
9
• = a closed dot means the number is included in the graph
10
11
12
13
10
11
12
13
Practice: Draw number lines on a sheet of
notebook paper. Graph each inequality on a
separate number line.
18) a < 15
19) b ≥ 7
20) 2 + y ≤ 3
21) w – 1 < 4
22)
r
>8
9